Driving across country in late January?

I'm going to be drivig from the SF Bay Area to New Hampshire in late January (moving). I did this trip before but it was in July so no weather concerns then. I'm from NH so I'm ok with driving in snow and I am allowing plenty of time. I know I won't make this trip in 4 days like I did before so I'm planning on taking my sweet time and taking it day by day, checking the weather before leaving, and just waiting out any storms. However, my car is only a Ford Focus. I'll put high traction tires on it and pack supplies and all that but I am still concerned about that first day or 2 through Tahoe and then Wyoming.
Should I be worried? Do I have an ok chance of finding a day with little to no snowfall or am I just doomed to see a storm any day? Anything I haven't considered yet?

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